Visualization of the 65536 first integer numbers with at least one '0' -black points- for the bases 2 -lower left- to 17 -upper right- (Visualisation des 65536 premiers nombres entiers avec au moins un '0' -points noirs- pour les bases 2 -en bas et a gauche- a 17 -en haut et a droite-) {a chapter of 'Mathematics - A Virtual Instrument For Exploring Space Time And Beyond'}

Visualization of the 65536 first integer numbers with at least one '0' -black points- for the bases 2 -lower left- to 17 -upper right- [Visualisation des 65536 premiers nombres entiers avec au moins un '0' -points noirs- pour les bases 2 -en bas et à gauche- à 17 -en haut et à droite-].

Starting from the origin of the coordinates (at the center of the picture), one follows a square spiral-like path and numbers each integer point encountered (1, 2, 3,...):

                    5----4----3
                    |         |    .
                    |         |    .
                    6    1----2    .
                    |              |
                    |              |
                    7----8----9----10

Then one displays the N-th point with the black "color" when N contains at least one '0' (by the way, for the base 2 every number N contains at least one '0' except the powers of 2 minus 1).

See some related pictures:

The multiplicative persistence of the 65536 first integer numbers for the bases 2 -lower left- to 17 -upper right-

Visualization of the 65536 first integer numbers with at least one '0' for the bases 6 -lower left- to 21 -upper right-

(CMAP28 WWW site: this page was created on 01/13/2015 and last updated on 06/04/2026 23:21:51 -CEST-)

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Copyright © Jean-François COLONNA, 2015-2026. Copyright © CMAP (Centre de Mathématiques APpliquées) UMR CNRS 7641 / École polytechnique, Institut Polytechnique de Paris, 2015-2026.

Copyright © Jean-François COLONNA, 2015-2026.
Copyright © CMAP (Centre de Mathématiques APpliquées) UMR CNRS 7641 / École polytechnique, Institut Polytechnique de Paris, 2015-2026.